Least Common Multiple (LCM) of 167 and 189
The least common multiple (LCM) of 167 and 189 is 31563.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 167 and 189?
First, calculate the GCD of 167 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 189 = 0 remainder 167 |
| 2 | 189 ÷ 167 = 1 remainder 22 |
| 3 | 167 ÷ 22 = 7 remainder 13 |
| 4 | 22 ÷ 13 = 1 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 162 | 810 |
| 104 and 139 | 14456 |
| 181 and 83 | 15023 |
| 197 and 46 | 9062 |
| 188 and 172 | 8084 |